الفهرس 
Introduction and historical surveyOnly 14 pages are availabe for public view
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Abstract
Many researchers have been drawn to vibration control in recent decades, prompting them to devote significant time and effort to investigate this topic. In this thesis, we concentrated on reducing and regulating vibrations caused by non - linear dynamical systems. These systems are composite cantilever beam, rotating beam structural model, an externally excited Duffing oscillator model, permanent magnet motor rotor system in shearer semi-direct drive cutting unite, and Pitch – Roll ship model. Different types of active controllers have been applied to these mentioned systems to control and minimize vibration amplitudes. In the composite cantilever beam, we applied an active control scheme, time delay feedback control on the velocity and on the displacement. This system of second order differential equations with non - linearity due to quadratic and cubic terms, excited by parametric and external excitations, is presented. The procedure of multiple time scales perturbation is used to achieve an estimated solution for this scheme. At this approximation order, all potential resonance cases are extracted and numerically investigated. Both frequency response formulas and phase-plane trajectories are used to assess the system’s stability during the worst resonance. The outcomes of various parameters on the device and controller are numerically investigated. The simulation results are achieved using Matlab and Maple programs. The timedependent displacements are provided, and excellent consensus is reached as compared to results produced utilizing the Rung-Kutta procedure.